Understanding the persistence of measles

Reconciling theory, simulation and observation

Matt J. Keeling, Bryan T. Grenfell

Research output: Contribution to journalArticle

98 Citations (Scopus)

Abstract

Ever since the pattern of localized extinction associated with measles was discovered by Bartlett in 1957, many models have been developed in an attempt to reproduce this phenomenon. Recently, the use of constant infectious and incubation periods, rather than the more convenient exponential forms, has been presented as a simple means of obtaining realistic persistence levels. However, this result appears at odds with rigorous mathematical theory; here we reconcile these differences. Using a deterministic approach, we parameterize a variety of models to fit the observed biennial attractor, thus determining the level of seasonality by the choice of model. We can then compare fairly the persistence of the stochastic versions of these models, using the 'best-fit' parameters. Finally, we consider the differences between the observed fade-out pattern and the more theoretically appealing 'first passage time'.

Original languageEnglish (US)
Pages (from-to)335-343
Number of pages9
JournalProceedings of the Royal Society B: Biological Sciences
Volume269
Issue number1489
DOIs
StatePublished - Feb 22 2002

Fingerprint

measles
Measles
persistence
Observation
simulation
mathematical theory
seasonality
extinction
incubation

All Science Journal Classification (ASJC) codes

  • Agricultural and Biological Sciences(all)
  • Environmental Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)

Cite this

@article{0c31fb616fce434dbfec943c2913c394,
title = "Understanding the persistence of measles: Reconciling theory, simulation and observation",
abstract = "Ever since the pattern of localized extinction associated with measles was discovered by Bartlett in 1957, many models have been developed in an attempt to reproduce this phenomenon. Recently, the use of constant infectious and incubation periods, rather than the more convenient exponential forms, has been presented as a simple means of obtaining realistic persistence levels. However, this result appears at odds with rigorous mathematical theory; here we reconcile these differences. Using a deterministic approach, we parameterize a variety of models to fit the observed biennial attractor, thus determining the level of seasonality by the choice of model. We can then compare fairly the persistence of the stochastic versions of these models, using the 'best-fit' parameters. Finally, we consider the differences between the observed fade-out pattern and the more theoretically appealing 'first passage time'.",
author = "Keeling, {Matt J.} and Grenfell, {Bryan T.}",
year = "2002",
month = "2",
day = "22",
doi = "https://doi.org/10.1098/rspb.2001.1898",
language = "English (US)",
volume = "269",
pages = "335--343",
journal = "Proceedings of the Royal Society B: Biological Sciences",
issn = "0962-8452",
publisher = "The Royal Society",
number = "1489",

}

Understanding the persistence of measles : Reconciling theory, simulation and observation. / Keeling, Matt J.; Grenfell, Bryan T.

In: Proceedings of the Royal Society B: Biological Sciences, Vol. 269, No. 1489, 22.02.2002, p. 335-343.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Understanding the persistence of measles

T2 - Reconciling theory, simulation and observation

AU - Keeling, Matt J.

AU - Grenfell, Bryan T.

PY - 2002/2/22

Y1 - 2002/2/22

N2 - Ever since the pattern of localized extinction associated with measles was discovered by Bartlett in 1957, many models have been developed in an attempt to reproduce this phenomenon. Recently, the use of constant infectious and incubation periods, rather than the more convenient exponential forms, has been presented as a simple means of obtaining realistic persistence levels. However, this result appears at odds with rigorous mathematical theory; here we reconcile these differences. Using a deterministic approach, we parameterize a variety of models to fit the observed biennial attractor, thus determining the level of seasonality by the choice of model. We can then compare fairly the persistence of the stochastic versions of these models, using the 'best-fit' parameters. Finally, we consider the differences between the observed fade-out pattern and the more theoretically appealing 'first passage time'.

AB - Ever since the pattern of localized extinction associated with measles was discovered by Bartlett in 1957, many models have been developed in an attempt to reproduce this phenomenon. Recently, the use of constant infectious and incubation periods, rather than the more convenient exponential forms, has been presented as a simple means of obtaining realistic persistence levels. However, this result appears at odds with rigorous mathematical theory; here we reconcile these differences. Using a deterministic approach, we parameterize a variety of models to fit the observed biennial attractor, thus determining the level of seasonality by the choice of model. We can then compare fairly the persistence of the stochastic versions of these models, using the 'best-fit' parameters. Finally, we consider the differences between the observed fade-out pattern and the more theoretically appealing 'first passage time'.

UR - http://www.scopus.com/inward/record.url?scp=53149094352&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=53149094352&partnerID=8YFLogxK

U2 - https://doi.org/10.1098/rspb.2001.1898

DO - https://doi.org/10.1098/rspb.2001.1898

M3 - Article

VL - 269

SP - 335

EP - 343

JO - Proceedings of the Royal Society B: Biological Sciences

JF - Proceedings of the Royal Society B: Biological Sciences

SN - 0962-8452

IS - 1489

ER -